Solve {l}{(x-y-z)(y-x-z)}{(z-x-y)}

$$\left. \begin{array} { l } { ( x - y - z ) ( y - x - z ) } \\ { ( z - x - y ) } \end{array} \right.$$

Least Common Multiple

$$\left(x-y-z\right)\left(-\left(z-y\right)^{2}+x^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$z^{2}-\left(x-y\right)^{2}=\left(x-y+z\right)\left(-x+y+z\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-y-z\right)\left(x+y-z\right)\left(x-y+z\right)$$

Expand the expression.

$$x^{3}-xy^{2}+2xyz-xz^{2}+y^{3}-yx^{2}-yz^{2}+z^{3}-zx^{2}-zy^{2}$$

Evaluate

$$-\left(x-y\right)^{2}+z^{2},\ z-y-x$$